Prime ideal quotient criterion
= Prime ideal quotient criterion
For a commutative unital ring $R$, an ideal $I$ is prime exactly when $R/I$ is an integral domain. The zero-product condition in the quotient translates directly to $ab\in I$.
= Prime ideal quotient criterion
For a commutative unital ring $R$, an ideal $I$ is prime exactly when $R/I$ is an integral domain. The zero-product condition in the quotient translates directly to $ab\in I$.